The Czech forward is struggling with excess fluid in his foot, which looks set to keep him out of Wednesday's crucial European showdown.
Hamsik has netted six times for Napoli in Serie A this term and has played a pivotal role in the Italian side's Champions League campaign to date.
Napoli must beat Premier League leaders Arsenal by three goals or more if they are to qualify for the knockout stages of the European competition.
However, Benitez admitted on Friday his side may have to overcome that hurdle without their influential playmaker.
"Marek has an oedema on his feet," he said. "It's not a serious thing but we must wait the right time to allow the problem to disappear.
"He won't play on Saturday and probably not at Arsenal either."
Napoli face Udinese this weekend and enter the tie six points adrift of league leaders Juventus after a recent dip in form, but Benitez insists minds are set on the task in hand.
"Our mind is only for this," he added. "The obstacle that arrives before is the one you must overcome and it's the most difficult one.
"My guys are aware that tomorrow's one will be a difficult game for us."